Sum rules and electron-electron interaction in two-center scattering

Abstract

The role of target-electronprojectile-electron interactions in projectile-electron loss is examined in the framework of the plane-wave-Born-approximation.The summation over target-electron states, which typically uses the closure approximation, is refined by using a sum rule for stopping power due to Bethe. The resulting expression for the cross section is compared with other modifications of the closure approximation and with the experimental H +H electron-loss section.

Effective Ion Charge

“…(16), (17) were discussed in Ref. [9] for the hydrogen-like one-electron ion form factor, Fi(q) = Nif(q), where F(q) = (1 + q2/4) -2 , q0 = 2/Ζ, Ni = 1.…”

“…(14), (15) the stopping is a sum of two components which are due to atom and projectile excitation and ionization, contrary to Eqs. (16), (17) where an ion-elastic collision with a frozen charge distribution on the projectile is assumed. This sum is a direct consequence of the model assumption that the eigenstate of the syStem is a product of component eigenstates, and the eigenenergy of the system is a sum of component eigenenergies.…”

Two-center electron-electron correlation within the independent event model

“…These comparisons are shown in figures 4 through 6, for the He + , Li 2+ and Li + projectiles, respectively. In these figures, the experimental data (solid triangles) are the same as in figures 1 to 3, respectively, the thick solid lines are the calculated total single-loss -single-ionization cross sections, the dotted lines are the contributions from the antiscreening calculated using equations (5) (He + ), (6) (Li 2+ ), and (7) (Li + ), and the dashed lines represent the antiscreening cross sections calculated according to Montenegro and Meyerhof within the PWBA [15]. Also included is the contribution of the direct loss-ionization (LI) process, i.e., the ionization of both partners due to the direct Coulomb nucleus-electron interaction (dash-dotted line), which was obtained by subtracting the antiscreening contribution from the total singleloss -single-ionization cross section.…”

“…In the calculations of all these probabilities, the effective atomic number and the ionization energies of the targets were taken from Refs. [47] and [48], respectively.The antiscreening probabilities, as functions of the impact parameter, were estimated from cross sections calculated using the procedure introduced by Montenegro and Meyerhof within the PWBA [15]. Since the antiscreening is due to the overlap of the electron clouds of the projectile and the target, it ranges up to rather large values of the impact parameter of the collision.…”

“…The pioneering works of Bates and Griffing [14] provided the first description of such electron-loss processes within the first-Born approximation. Actually, the behavior of both the screening and the antiscreening modes for light targets is conveniently described by first-order models, such as the plane wave Born approximation (PWBA) [2,3,15,16,17].There are not many options available to treat collision systems with several potentially active electrons as a whole, mainly in collisions where the probabilities for several of the competing processes are of the same order of magnitude and, thus, have to be considered simultaneously, since they are no longer independent. If more than one electron undergo a transition, the description is obviously more complicated, since one needs to couple, in principle in an unitarized way, the probabilities of occurrence of each transition.…”